The time-integrated untagged Dalitz plot of the three-body hadronic charmless decay B[over ¯]^{0}→K_{S}^{0}π^{+}π^{-} is studied using a pp collision data sample recorded with the LHCb detector, corresponding to an integrated luminosity of 3.0 fb^{-1}. The decay amplitude is described with an isobar model. Relative contributions of the isobar amplitudes to the B[over ¯]^{0}→K_{S}^{0}π^{+}π^{-} decay branching fraction and CP asymmetries of the flavor-specific amplitudes are measured. The CP asymmetry between the conjugate B[over ¯]^{0}→K^{*}(892)^{-}π^{+} and B^{0}→K^{*}(892)^{+}π^{-} decay rates is determined to be -0.308±0.062.